Hello Everyone,

Given a string s, print all possible subsequences of the given string in an iterative manner.

**Examples:**

Input : abc Output : a, b, c, ab, ac, bc, abc Input : aab Output : a, b, aa, ab, aab

**Approach 1 :**

Here, we discuss much easier and simpler iterative approach which is similar to Power Set. We use bit pattern from binary representation of 1 to 2^length(s) – 1.

input = “abc”

Binary representation to consider 1 to (2^3-1), i.e 1 to 7.

Start from left (MSB) to right (LSB) of binary representation and append characters from input string which corresponds to bit value 1 in binary representation to Final subsequence string sub.

Example:

001 => abc . Only c corresponds to bit 1. So, subsequence = c.

101 => abc . a and c corresponds to bit 1. So, subsequence = ac.

binary_representation (1) = 001 => c

binary_representation (2) = 010 => b

binary_representation (3) = 011 => bc

binary_representation (4) = 100 => a

binary_representation (5) = 101 => ac

binary_representation (6) = 110 => ab

binary_representation (7) = 111 => abc

Below is the implementation of above approach:

`// C++ program to print all Subsequences`

`// of a string in iterative manner`

`#include <bits/stdc++.h>`

`using`

`namespace`

`std;`

`// function to find subsequence`

`string subsequence(string s, `

`int`

`binary, `

`int`

`len)`

`{`

` `

`string sub = `

`""`

`;`

` `

`for`

`(`

`int`

`j = 0; j < len; j++)`

` `

`// check if jth bit in binary is 1`

` `

`if`

`(binary & (1 << j))`

` `

`// if jth bit is 1, include it`

` `

`// in subsequence`

` `

`sub += s[j];`

` `

`return`

`sub;`

`}`

`// function to print all subsequences`

`void`

`possibleSubsequences(string s){`

` `

`// map to store subsequence`

` `

`// lexicographically by length`

` `

`map<`

`int`

`, set<string> > sorted_subsequence;`

` `

`int`

`len = s.size();`

` `

` `

`// Total number of non-empty subsequence`

` `

`// in string is 2^len-1`

` `

`int`

`limit = `

`pow`

`(2, len);`

` `

` `

`// i=0, corresponds to empty subsequence`

` `

`for`

`(`

`int`

`i = 1; i <= limit - 1; i++) {`

` `

` `

`// subsequence for binary pattern i`

` `

`string sub = subsequence(s, i, len);`

` `

` `

`// storing sub in map`

` `

`sorted_subsequence[sub.length()].insert(sub);`

` `

`}`

` `

`for`

`(`

`auto`

`it : sorted_subsequence) {`

` `

` `

`// it.first is length of Subsequence`

` `

`// it.second is set<string>`

` `

`cout << `

`"Subsequences of length = "`

` `

`<< it.first << `

`" are:"`

`<< endl;`

` `

` `

`for`

`(`

`auto`

`ii : it.second)`

` `

` `

`// ii is iterator of type set<string>`

` `

`cout << ii << `

`" "`

`;`

` `

` `

`cout << endl;`

` `

`}`

`}`

`// driver function`

`int`

`main()`

`{`

` `

`string s = `

`"aabc"`

`;`

` `

`possibleSubsequences(s);`

` `

`return`

`0;`

`}`

**Output:**

Subsequences of length = 1 are: a b c Subsequences of length = 2 are: aa ab ac bc Subsequences of length = 3 are: aab aac abc Subsequences of length = 4 are: aabc

Time Complexity : O(2^{n} * l) , where n is length of string to find subsequences and l is length of binary string.

**Approach 2 :**

Approach is to get the position of rightmost set bit and and reset that bit after appending corresponding character from given string to the subsequence and will repeat the same thing till corresponding binary pattern has no set bits.

If input is s = “abc”

Binary representation to consider 1 to (2^3-1), i.e 1 to 7.

001 => abc . Only c corresponds to bit 1. So, subsequence = c

101 => abc . a and c corresponds to bit 1. So, subsequence = ac.

Let us use Binary representation of 5, i.e 101.

Rightmost bit is at position 1, append character at beginning of sub = c ,reset position 1 => 100

Rightmost bit is at position 3, append character at beginning of sub = ac ,reset position 3 => 000

As now we have no set bit left, we stop computing subsequence.

Example :

binary_representation (1) = 001 => c

binary_representation (2) = 010 => b

binary_representation (3) = 011 => bc

binary_representation (4) = 100 => a

binary_representation (5) = 101 => ac

binary_representation (6) = 110 => ab

binary_representation (7) = 111 => abc

Below is the implementation of above approach :

`// C++ code all Subsequences of a`

`// string in iterative manner`

`#include <bits/stdc++.h>`

`using`

`namespace`

`std;`

`// function to find subsequence`

`string subsequence(string s, `

`int`

`binary)`

`{`

` `

`string sub = `

`""`

`;`

` `

`int`

`pos;`

` `

` `

`// loop while binary is greater than 0`

` `

`while`

`(binary>0)`

` `

`{`

` `

`// get the position of rightmost set bit`

` `

`pos=log2(binary&-binary)+1;`

` `

` `

`// append at beginning as we are`

` `

`// going from LSB to MSB`

` `

`sub=s[pos-1]+sub;`

` `

` `

`// resets bit at pos in binary`

` `

`binary= (binary & ~(1 << (pos-1)));`

` `

`}`

` `

`reverse(sub.begin(),sub.end());`

` `

`return`

`sub;`

`}`

`// function to print all subsequences`

`void`

`possibleSubsequences(string s){`

` `

`// map to store subsequence`

` `

`// lexicographically by length`

` `

`map<`

`int`

`, set<string> > sorted_subsequence;`

` `

`int`

`len = s.size();`

` `

` `

`// Total number of non-empty subsequence`

` `

`// in string is 2^len-1`

` `

`int`

`limit = `

`pow`

`(2, len);`

` `

` `

`// i=0, corresponds to empty subsequence`

` `

`for`

`(`

`int`

`i = 1; i <= limit - 1; i++) {`

` `

` `

`// subsequence for binary pattern i`

` `

`string sub = subsequence(s, i);`

` `

` `

`// storing sub in map`

` `

`sorted_subsequence[sub.length()].insert(sub);`

` `

`}`

` `

`for`

`(`

`auto`

`it : sorted_subsequence) {`

` `

` `

`// it.first is length of Subsequence`

` `

`// it.second is set<string>`

` `

`cout << `

`"Subsequences of length = "`

` `

`<< it.first << `

`" are:"`

`<< endl;`

` `

` `

`for`

`(`

`auto`

`ii : it.second)`

` `

` `

`// ii is iterator of type set<string>`

` `

`cout << ii << `

`" "`

`;`

` `

` `

`cout << endl;`

` `

`}`

`}`

`// driver function`

`int`

`main()`

`{`

` `

`string s = `

`"aabc"`

`;`

` `

`possibleSubsequences(s);`

` `

` `

`return`

`0;`

`}`

**Output:**

Subsequences of length = 1 are: a b c Subsequences of length = 2 are: aa ab ac bc Subsequences of length = 3 are: aab aac abc Subsequences of length = 4 are: aabc

Time Complexity: O(2^{n} * b) , where n is the length of string to find subsequence and b is the number of set bits in binary string.